Fractional time random walk subdiffusion and anomalous transport with finite mean residence times: faster, not slower

Abstract

Continuous time random walk (CTRW) subdiffusion along with the associated fractional Fokker-Planck equation (FFPE) is traditionally based on the premise of random clock with divergent mean period. This work considers an alternative CTRW and FFPE description which is featured by finite mean residence times (MRTs) in any spatial domain of finite size. Transient subdiffusive transport can occur on a very large time scale ${\tau }_c$ which can greatly exceed mean residence time in any trap, ${\tau }_c\gg <\tau >$, and even not being related to it. Asymptotically, on a macroscale transport becomes normal for $t\gg {\tau }_c$. However, mesoscopic transport is anomalous. Differently from viscoelastic subdiffusion no long-range anti-correlations among position increments are required. Moreover, our study makes it obvious that the transient subdiffusion and transport are faster than one expects from their normal asymptotic limit on a macroscale. This observation has profound implications for anomalous mesoscopic transport processes in biological cells because of macroscopic viscosity of cytoplasm is finite.

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